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Seeking to answer the question of how much one should trust the predictions made by models and algorithms, and whether they are trustworthy enough for design and decision-making tasks, professors Markos Katsoulakis and Luc Rey-Bellet, mathematics and statistics, with applied mathematics professor Paul Dupuis at Brown University, recently received a three-year, $900,000 grant from the Air Force’s Office of Scientific Research to develop mathematical tools to assess and improve the predictive performance of complex mathematical and computational models. The UMass component is $600,000.

Katsoulakis explains that probabilistic computational models are currently a primary discovery tool for understanding and predicting complex phenomena in weather, traffic patterns, social networks, finance, chemistry, life sciences and other fields. Though potentially powerful, computational models are susceptible to errors and uncertainty, since they have to model highly complex systems with millions or even billions of variables and parameters, and must be informed by available data across different scales.

He says the work is immediately applicable to computational chemistry and materials science problems where there is a need to piece together computational models with data from different scales, from quantum to mesoscale to macroscopic or “real life” scale. Key mathematical tools to provide performance guarantees include uncertainty quantification, information theory, robust optimization, extreme events and approximate inference.

Specifically, for this grant the researchers will investigate the effect of model and data uncertainties in materials science problems with multiple spatio-temporal scales, such as understanding how uncertainties at the quantum level propagate to meso- and macro-scales, and the impact of rare and extreme events on predictions. Further, they intend to provide reliable computational strategies for design and optimization under uncertainty focused on energy research problems such as designing better batteries, thermoelectric devices and fuel cells.

An important feature of their effort to build more reliable computational models, they plan to address the predictive accuracy of machine learning algorithms, using similar mathematical, statistical and computational tools. Katsoulakis says, “A notable and important example across application domains of machine learning methods that we plan to address is providing prediction guarantees for classes of approximate inference algorithms such as variational inference and expectation propagation methods.”